Even without spending talent points, all Shamans can buff their group for many purposes (e.g. a Restoration Shaman can drop Windfury Totem just like as an Enhancement Shaman).

By spending talent points, shamans increase the efficiency of these group buffs, and some buffs can be gained only by spending points.

The leveling spec chosen by most shamans is Enhancement. The main advantage when leveling with this build is that it requires next to no downtime. An Enhancement Shaman relies mostly on melee damage, and spends only low amounts of mana during combat, keeping the mana pool as an emergency reserve, and to heal up between combats.

Elemental is typically the tree of choice for PvP shamans who want to deal damage. It's also chosen by many "hybrid" players, because it offers a nice equipment synergy with the Restoration tree. Shamans may consider to give up Totem of Wrath in order to get Nature's Swiftness from the Restoration tree.
Note: As of patch 3.1 Nature's Swiftness shares a cooldown with Elemental Mastery making this talent build far less favorable.

Restoration is the Healing tree, turning shamans into very capable healers for PvE and PvP alike.

Elemental is the Shaman's caster DPS spec. It specializes in dealing damage from afar. Some notable talents are Elemental Mastery allowing the shaman to instant cast a damaging spell, and Thunderstorm which is infamous for throwing members of the opposing faction to their death.

You call down a bolt of lightning, energizing you and damaging nearby enemies within 10 yards. Restores 8% mana to you and deals X Nature damage to all nearby enemies, knocking them back 20 yards. This spell is usable while stunned.

Protects the target with an earthen shield, reducing casting or channeling time lost when damaged by 30% and causing attacks to heal the shielded target for X. This effect can only occur once every few seconds. 9 charges. Lasts 10 minutes. Earth Shield can only be placed on one target at a time and only one ElementalShield can be active on a target at a time.

While Water Shield is active, you recover mana when your direct healing spells have a critical effect. You regain X mana from a Healing Wave or Greater Healing Wave critical, X * 0.6 mana from a Healing Surge, Riptide, or Unleash Life critical, and X * 0.333 mana from a Chain Heal critical.

Whenever a damaging attack is taken that reduces you below 30% health, you have a 100% chance to increase your maximum health by X% for 10 seconds and reduce your threat level on that target. 30 second cooldown.

When you critically heal with a single-target direct heal, you summon an Ancestral spirit to aid you, instantly healing the lowest percentage health party or raid target with in 40 yards for for X% of the amount healed.

Summons a Spirit Link Totem with 5 health at the feet of the caster. The totem reduces damage taken by all party and raid members within 10 yards by 10%. Every 1 sec, the health of all affected players is redistributed, such that each player ends up with the same percentage of their maximum health. Lasts 6 sec.

When you cast Chain Heal or Riptide, you gain the tidal wave effect, which reduces the cast time of your Healing Wave and Greater Healing Wave by X% and increase the critical effect chance of your Healing surge by X%, until two such spells have been cast.

Heals a friendly target for X and another Y over 15 sec. Your next Chain Heal cast on that primary target within 15 sec will consume the healing over time effect and increase the amount of the Chain Heal by 25%.